Finding Shortest Path on a Terrain Surface by Using Finite Element Method

The solution of the shortest path problem on a surface is not only a theoretical problem to be solved in the field of mathematics, but also problems that need to be solved in very different fields such as medicine, defense and construction technologies. When it comes to the land specific, solution algorithms for these problems are also of great importance in terms of determination of the shortest path in an open area where the road will pass in the field of civil engineering, or route determination of manned or unmanned vehicles for various logistic needs, especially in raw terrains. In addition, path finding problems in the raw terrains are also important for manned and unmanned ground vehicles (UGV) used in the defense industry. Within the scope of this study, a method that can be used for instant route determinations within sight range or for route determinations covering wider areas is proposed. Although the examples presented within the scope of the study are land-based, the method can be applied to almost all problem types of similar nature. The approach used in the study can be briefly described as the mechanical analysis of a surface transformed into a structural load bearing system based on mechanical analogies. In this approach, the determination of the shortest path connecting two points can be realized by following the stress-strain values that will occur by moving the points away from each other or by following a linear line that will be formed between two points during the mechanical analysis. If the proposed approach is to be carried out with multiple rigid body dynamics approaches instead of flexible bodies mechanics, it can be carried out easily and very quickly by determining the shortest path between two points or by tracking the forces. However, the proposed approach in this study is presented by simulating examples of flexible bodies using FEM.